Big Bang Observer and the neutron-star-binary subtraction problem

The Big Bang Observer (BBO) is a proposed space-based gravitational-wave (GW) mission designed primarily to search for an inflation-generated GW background in the frequency range $\ensuremath{\sim}{10}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Hz}--1\text{ }\text{ }\mathrm{Hz}$. The major astrophysical foreground in this range is gravitational radiation from inspiralling compact binaries. This foreground is expected to be much larger than the inflation-generated background, so to accomplish its main goal, BBO must be sensitive enough to identify and subtract out practically all such binaries in the observable universe. It is somewhat subtle to decide whether BBO's current baseline design is sufficiently sensitive for this task, since, at least initially, the dominant noise source impeding identification of any one binary is confusion noise from all the others (rather than instrumental noise). Here we present a self-consistent scheme for deciding whether BBO's baseline design is indeed adequate for subtracting out the binary foreground. We conclude that the current baseline should be sufficient. However, if BBO's sensitivity were degraded by a factor 2 from the current baseline, then its ability to detect an underlying primordial background would depend critically on the value of ${\ensuremath{\rho}}_{\mathrm{th}}$, the threshold signal-to-noise ratio marking the boundary between detectable and undetectable sources. If BBO's sensitivity were degraded by a factor 4 from the current baseline, it could not detect a primordial background below ${\ensuremath{\Omega}}_{\mathrm{GW}}\ensuremath{\sim}{10}^{\ensuremath{-}15}$. It is impossible to perfectly subtract out each of the binary inspiral waveforms, so an important question is how to deal with the ``residual'' errors in the post-subtraction data stream. We sketch a strategy of ``projecting out'' these residual errors, at the cost of some effective bandwidth. We also provide estimates of the sizes of various post-Newtonian effects in the inspiral waveforms that must be accounted for in the BBO analysis.